Complex Variables & Applications Text-Book || Free Download In PDF

Complex Variables And Applications Text-Book

Complex Variables & Applications Text-Book || Free Download In PDF

Complex variables & applications textbook by James Ward Brown & Ruel V. Churchill for MS.c/BS mathematics in pdf form. This book contains all important topics according to paper guidelines. 
Mathematics has evolved over many centuries to help solve problems. 
Math teaches us to think logically; identify and state the problem clearly; plan how to solve the problem, and then apply the appropriate methods to evaluate and solve the problem. There, we are providing you Complex Variables and Applications book in pdf form.  

1. Complex Numbers 

  • Sums and Products 1
  • Basic Algebraic Properties 3
  • Further Properties 5
  • Vectors and Moduli 9
  • Complex Conjugates 13
  • Exponential Form 16
  • Products and Powers in Exponential Form 18
  • Arguments of Products and Quotients 20
  • Roots of Complex Numbers 24
  • Examples 27
  • Regions in the Complex Plane 31

                    2. Analytic Functions 

                    • Functions of a Complex Variable 35
                    • Mappings 38
                    • Mappings by the Exponential Function 42
                    • Limits 45
                    • Theorems on Limits 48
                    • Limits Involving the Point at Infinity 50
                    • Continuity 53
                    • Derivatives 56
                    • Differentiation Formulas 60
                    • Cauchy–Riemann Equations 63
                    • Sufficient Conditions for Differentiability 66
                    • Polar Coordinates 68
                    • Analytic Functions 73
                    • Examples 75
                    • Harmonic Functions 78
                    • Uniquely Determined Analytic Functions 83
                    • Reflection Principle 85

                    3. Elementary Functions 

                    • The Exponential Function 89
                    • The Logarithmic Function 93
                    • Branches and Derivatives of Logarithms 95
                    • Some Identities Involving Logarithms 98
                    • Complex Exponents 101
                    • Trigonometric Functions 104
                    • Hyperbolic Functions 109
                    • Inverse Trigonometric and Hyperbolic Functions 112

                    4. Integrals

                    • Derivatives of Functions w(t) 117
                    • Definite Integrals of Functions w(t) 119
                    • Contours 122
                    • Contour Integrals 127
                    • Some Examples 129
                    • Examples with Branch Cuts 133
                    • Upper Bounds for Moduli of Contour Integrals 137
                    • Antiderivatives 142
                    • Proof of the Theorem 146
                    • Cauchy–Goursat Theorem 150
                    • Proof of the Theorem 152
                    • Simply Connected Domains 156
                    • Multiply Connected Domains 158
                    • Cauchy Integral Formula 164
                    • An Extension of the Cauchy Integral Formula 165
                    • Some Consequences of the Extension 168
                    • Liouville’s Theorem & the Fundamental Theorem of Algebra 172
                    • Maximum Modulus Principle 175

                    5. Series

                    • Convergence of Sequences 181
                    • Convergence of Series 184
                    • Taylor Series 189
                    • Proof of Taylor’s Theorem 190
                    • Examples 192
                    • Laurent Series 197
                    • Proof of Laurent’s Theorem 199
                    • Examples 202
                    • Absolute and Uniform Convergence of Power Series 208
                    • Continuity of Sums of Power Series 211
                    • Integration and Differentiation of Power Series 213
                    • The uniqueness of Series Representations 217
                    • Multiplication and Division of Power Series 222

                    6. Residues and Poles 

                    • Isolated Singular Points 229
                    • Residues 231
                    • Cauchy’s Residue Theorem 234
                    • Residue at Infinity 237
                    • The Three Types of Isolated Singular Points 240
                    • Residues at Poles 244
                    • Examples 245
                    • Zeros of Analytic Functions 249
                    • Zeros and Poles 252
                    • The behavior of Functions Near Isolated Singular Points 257

                    7. Applications of Residues

                    • Evaluation of Improper Integrals 261
                    • Example 264
                    • Improper Integrals from Fourier Analysis 269
                    • Jordan’s Lemma 272
                    • Indented Paths 277
                    • An Indentation Around a Branch Point 280
                    • Integration Along a Branch Cut 283
                    • Definite Integrals Involving Sines and Cosines 288
                    • Argument Principle 291
                    • Rouche’s Theorem 294  ́
                    • Inverse Laplace Transforms 298
                    • Examples 301

                    8. Mapping by Elementary Functions

                    • Linear Transformations 311
                    • The Transformation w = 1/z 313
                    • Mappings by 1/z 315
                    • Linear Fractional Transformations 319
                    • An Implicit Form 322
                    • Mappings of the Upper Half Plane 325
                    • The Transformation w = sin z 330
                    • Mappings by z2 and Branches of z1/2 336
                    • Square Roots of Polynomials 341
                    • Riemann Surfaces 347
                    • Surfaces for Related Functions 351

                    9. Conformal Mapping

                    • Preservation of Angles 355
                    • Scale Factors 358
                    • Local Inverses 360
                    • Harmonic Conjugates 363
                    • Transformations of Harmonic Functions 365
                    • Transformations of Boundary Conditions 367

                    10. Applications of Conformal Mapping

                    • Steady Temperatures 373
                    • Steady Temperatures in a Half Plane 375
                    • A Related Problem 377
                    • Temperatures in a Quadrant 379
                    • Electrostatic Potential 385
                    • Potential in a Cylindrical Space 386
                    • Two-Dimensional Fluid Flow 391
                    • The Stream Function 393
                    • Flows Around a Corner and Around a Cylinder 395

                    11. The Schwarz–Christoffel Transformation

                    • Mapping the Real Axis Onto a Polygon 403
                    • Schwarz–Christoffel Transformation 405
                    • Triangles and Rectangles 408
                    • Degenerate Polygons 413
                    • Fluid Flow in a Channel Through a Slit 417
                    • Flow in a Channel With an Offset 420
                    • Electrostatic Potential About an Edge of a Conducting Plate 422

                    12. Integral Formulas of the Poisson Type

                    • Poisson Integral Formula 429
                    • Dirichlet Problem for a Disk 432
                    • Related Boundary Value Problems 437
                    • Schwarz Integral Formula 440
                    • Dirichlet Problem for a Half Plane 441
                    • Neumann Problems 445

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